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Figure 1. Albert Einstein

Another Tribute To Albert Einstein:
Achievement of an attractive force between identical valence electrons via Einstein's 'completion' of quantum mechanics

A PubRelco Interview of Sir Ruggero Maria Santilli. with Scientific and Industrial implications.

New York, N.Y., April 15, 2019

Q1. Prof. Santilli, could you please review in a language accessible to the general audience Einstein's 1935 historical prediction that quantum mechanics and, therefore, quantum chemistry are incomplete theories

A1. Einstein did not accept the uncertainty of quantum mechanics, including the impossibility to identify the position of a particle with classical precision. For that reason, he made his famous quote "God does not play dice with the universe." Einstein accepted quantum mechanics for atomic structures, but believed that quantum mechanics is an "incomplete theory," in the sense that it could be broadened into such a form to recover classical determinism at least under special conditions. The same argument evidently applies to quantum chemistry.

Q2. We understand that you proved Einstein's vision in physics.

A2. Yes, as reported in your preceding interview, I provided three physical broadening of quantum mechanics along Einstein's vision, the first was done by including irreversibility over time of energy releasing processes, the second was done via the representation of particles as they are in the physical reality (extended, deformable and hyperdense), and the third was done via a realization of quanrtum axioms admitting an explicit and concrete realization of the so-called 'hidden variables.' I also provided examples of particle pairs whose mutual distance a[[ears to recover indeed classical determinism under extreme conditions, as predicted by Einstein.


Figure 2. A conceptual rendering of the hydrogen molecule at absolute zero degree temperature without the bond of valence electrons showing no attractive or repulsive force between the two atoms..

Q3. Are you claiming to have proved Einstein's vision also in chemistry?

A3. Einstein's vision on the lack of final character of quantum mechanics has implications for all of 20th century sciences. Therefore, the lack of confirmation of Einstein's argument in chemistry would imply the lack of actual achievement of Einstein's vision.


Figure 3. A conceptual rendering of the hydrogen molecule according to quantum chemistry showing the repulsion (rather than a bond) between two point-like valence electrons due to their equal charge.

Q4. Can you please outline the main aspect of the confirmation in chemistry?

A4. With the understanding that quantum chemistry did achieve historical advances, I did not accept quantum chemistry as being a final theory since my graduate studies at the University of Torino, Italy, in the mid 1960s, because of a truly fundamental insufficiency, namely, the inability by quantum chemistry to identify the attractive force bonding together identical valence electrons. Consider, for simplicity, the hydrogen molecule H2 at absolute zero degree temperature. When the two electrons move in independent orbits (Figure 1), the hydrogen molecule cannot exist due to the absence of any possible bond. The two hydrogen atoms are bonded into the H2 molecure by the bond between the two valence electrons with antiparallel spin. By following Einstein, I could not consider quantum chemistry to be a complete theory because according to the basic axioms of quantum mechanics and chemistry, valence electrons should 'repel' each other due to their equal charge, without any known possibility of admitting their attraction (Figure 2). There was no doubt in my mind that the understanding of the attractive force between valence electrons required a 'completion' of quantum chemistry precisely along Einstein's vision. Following decades of research including contributions by various colleagues, quantum chemistry was completed into a covering theory known as hadronic chemistry; the attractive force between valence electrons was clearly identified; and the 'completed' theory was proved to verify molecular experimental data..


Figure 4. A conceptual rendering of the hydrogen molecule according to the completion of quantum chemistry into hadronic chemistry illustrating the first and only known attractive force between valence electrons caused by non-potential interactions due to deep entanglement of extended wavepackets .

Q5. Can you please outline the main steps of the indicated achievements?

A5. Evidence establishes the existence of a strongly attractive force between valence electron pairs. This can only occur via a interactions not derivable from a potential, thus not being representable with quantum chemistry. Hence, the representation of the new attractive force could only be done by 'completing' quantum chemistry into a broader theory admitting non-potential interactions.

Q6. How did you achieve the needed 'completion' of quantum chemistry?

A6. I accepted the evidence hat valence electrons are not point -particles as represented by quantum chemistry (Figures 1 and 2), because they are characterized by wavepackets that, technically, fill up the entire universe, of course, with an intensity inversely proportional to the distance. I also accepted the experimental evidence that the wavepackets of valence electrons are in conditions of deep mutual penetration also called entanglement (Figure 3). This allowed me to identify the new force as being of contact type, thus not being derivable from a potential.

Q7. How did you develop these ideas into a viable 'completion' of quantum chemistry?

A7. The biggest difficulty was mathematical, rather than chemical, because the mathematics of quantum chemistry can only represent potential forces between point particles. A mathematics for the representation of non-potential forces between extended valence electrons did not exist and, therefore, had to be built. When I was at the Department of Mathematics of Harvard University inn the late 1970s under DOE support, I initiated the construction of a new mathematics based on the generalization of all products AB between arbitrary quantities A, B, into the form A*B = ATB called 'isotopic' in the sense of being axiom-preserving, where T represents precisely the new non-potential forces (see my 1978 monographs with Springer-Verlag Foundation of Theoretical Mechanics, particularly Volume II). This allowed Einstein's 'completion' of the mathematics of quantum chemistry into a form admitting the d new forces. Applications and verifications were done thereafter.

Q8. Please outline the main chemical aspects with links to technical publication for interested chemists.

A8. The new forces were first identified in physics and verified with the representation of the synthesis of mesons (see Section 5 of the 1978 Harvard paper). Following that, In collaboration with the University of Cambridge Ph. D. physicist A. O. E. Animalu, we applied the new mathematics to the representation of the attractive force between the identical electrons of the Cooper pair in superconductivity (see the 1985 paper). In view of encouraging results in superconductivity, systematic studies lead to the first and only known 'attractive force' between valence electrons pairs in molecular structures nowadays known as the isoelectronium (see the 2001 monograph Foundations of Hadronic Chemistry, see also the independent reviews by V. M. Tandge, and by E. Trell). In collaboration with the chemist Don D. Shillady of Virginia Commonwealth University, we proved that the 'completion' of quantum chemical models into the form admitting an explicitly attractive force between valence electron pairs achieved an exact representation of experimental data of the hydrogen molecule, and of the water molecule.


Figure 5. From the left, Profs. R. M. Santilli, A. O. E. Animalu and D. D. Shillady.

Q9. Could you please indicate how the representation of the hydrogen molecule according to Figure 3 verifies Einstein's argument?

A9. When the two point-like valence electrons have independent orbits as in Figure 1, quantum mechanics is valid and classical determinism is impossible.. By contrast, when the two valence electrons are represented as extended entangled particles under non-potential forces as in Figure 3. the mathematics (let alone the physics) underlying the uncertainty principle is inapplicable (see Post 10 of the preceding interview), and the mutual distance between the two valence electrons approaches classical determinism. When in the interior odf a star, the same pair of entangled electrons comes closed to classical determinism and, when inside a black hole, the same pair verifies classical determinism in my view due to the extremely large pressures preventing any motiomn.

Q10. Does the academic community admit the lack of an actual bond in the hydrogen molecule according to quantum chemistry?

A10. No. The indicated insufficiency is a best kept secret in the best graduate schools in chemistry around the world.

Q11. Can you indicate the reaction by chemists to your achievement of an explicitly attractive force between valence electrons?

A11. With due exceptions, the reaction by chemists has generally been that of extreme repulsion because, in academia, basic novelty is an enemy to be assassinated at whatever cost. But I believe that such a negative reaction is a rather normal part of the scientific process for basically new advances and that, sooner or later, scientific evidence always emerges.

     

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COMMENTS

Post 1
Dear Editors, please ask Prof. Santilli how he achieved an attractive force between identical valence electrons. An outline for non-experts would be appreciated. Vdr39yu

Post 2
Hello Vdr39yu - Post 1, thanks for the important question. The isoelectronium is studied in details in Chapter 4 of Foundations of Hadronic Chemistry. The subsequent chapters provide verifications with molecular experimental data for the hydrogen and water molecules. Here is a rudimentary outline. After years of trials and failures with conventional methods, I had to conclude that there is no possibility to achieve an attractive force between identical electrons via the use of the Schroedinger equation of quantum chemistry,

H(r, p) ψ = E ψ,   H = K + V,     (1)

where H is the Hamiltonian of the valence electron pair as the sum of the kinetic energy K and the repulsive potential energy V. I achieved the needed attractive force via the use of the covering iso-schroedinger equation of hadronic chemistry

H(r, p) T(ψ*, ...)ψ* = E* ψ*,   H = K + V,     (2)

where H represents the conventional Coulomb interaction and T represents the new non-Hamiltonian interaction. Out of a variety of solutions, the simplest one occurs for (see. Eq. (4.7), loc, cit.)

T ≈ N eψ/ψ* ≈ 1 + N ψ/ψ* > 0     (3)

where N is a positive constant, ψ is the wavefunction of the quantum electron pair (1) and ψ* is an isowavefunction selected in such a way to achieve the desired attraction. Simple calculations yield the following solution

ψ* = M(1 - e- b r)/ r     (4)

where b = 1/rhh is the inverse of the 'hadronic horizon' rhh (the radius after which quantum mechanics is recovered identically because particles return to have sole potential interactions). Additional simple calculations via the use of Eq. (2) yield

H(r, p) T(ψ*, ...) ψ* ≈ (p2/m + e2/r + VHulten) ψ* = E' ψ*,     (5)

VHulten = 1 - Q[1 - e- br/(1 - e-br)/r]     (6)

where m is the mass of an electron.

The following points are then important for the plausibility of the model:

    1) The attractive Hulten potential behaves like the Coulomb one at short distance, thus absorbing the repulsive Coulomb potential in Eq. (5) resulting in the desired attraction with a mere re-definition of the Hulten constant Q.

   2) As it is well known, the Hulten potential has a finite number of energy states. Hence, there can only exist a finite number of isoelectronia.

| E' | = A(B/n - n)2 > 0,     (7)

where A and B are positive quantities depending on various local values, see for details Eq.s (5,15) page 171 of [loc. cit.].

   3) The application of the model, which i did with Don Shillady, to the representation of the experimental data of the hydrogen molecule, and of the water molecule yields numerical values of the A and B quantities, in particular, the value B = 1 under which spectrum (7) is reduced to one single value for n = 1. Therefore, the isoelectronium can assume one and only one configuration.

A few words of caution are now in order. The isoelectronium can only be formulated via hadronic chemistry and its underlying new isomathematics. The lack of knowledge of these methods generally results in inconsistencies that often remain unknown to users of conventional methods In fact, rudimentary Eqs. (2) to (7) are expressed via conventional mathematics but they are the projection of the actual equations on isospaces over isofields.

For instance, for the correct formulation of Eq. (2), coordinates r have to be isocoordinates r* - rU, where U is the isounit, U = 1/T; momenta p have to be isomomenta p* formulated via the isodifferential calculus; the Hamiltonian and other operators have to be isooperators defined on an iso-Hilbert isospace over the isofield of isocomplex isonumbers, etc. My suggestion is to understand first the mechanism for achieving the needed attractive forces between identical electrons and then pass to its rigorous formulation. Best wishes. Ruggero M. Santilli (Email: research@thunder-energies.com).

Post 3
Prof. Santilli, please indicate how the isoelectronium constitutes a verification of the EPR argument. Thanks. Lwe29ty


Figure 6. A conceptual rendering of the structure of the isoelectronium denoting two valence electrons with antiparallel spins under deep penetration of their wavepackets, as occurring in reality.

Post 4
Lwe29ty - Post 3, I am glad to see that this open exchange does indeed stimulate important questions. Here is my view. When the electrons are represented as point-like particles, quantum mechanics applies, and the EPR argument is inapplicable. However, when the electrons are represented with extended wavepackets in condition of mutual penetration, the sole existence of one energy level of the Hulten spectrum, Post 2, their mutual distance (see Figure 6) can only have one value, such as 10-15 cm, thus recovering classical determinism in clinet with Einstein's vision. Ruggero Maria Santilli (Email: research@thunder-energies.com).

Post 5
Prof. Santilli, thank you for the clear outline of Post 2 and congrats for a rather difficult achievement. I would appreciate more details on the structure of the isoelectronium, for instance, how you handle the non-linear interactions of hadronic chemistry clearly expressed in Eq. (2). Vdr39yu

Post 6
Hello Vdr39yu - Post 5, I appreciate your interest. You are sharp in seeing that a most crucial aspect of Eq. (2) is its non-linearity in the wavefunction ψ* . It should be recalled here that non-linear equations in quantum chemistry

H(r, p, ψ)ψ = E ψ     (8)

violates the superposition principle, thus preventing the decomposition of the wavefunction ψ of the isoelectronium into those of the two valence electrons,

ψ ≠ Col.(ψ1, ψ2)    (9)

This insufficiency prevents the identification of the characteristics of the constituents of a bound state with non-linear interactions (in our case, the valence electrons when members of a valence bond). This and other limitations have caused the general lack ion consideration of non-linear interactions in quantum chemistry.

A reason I could not accept quantum chemistry as a final theory is that it is linear in the wavefunction, while chemical reality is expected to be non-linear, particularly in the case of deep mutual penetration of the wavepackets in valence bonds where interactions are non-linear, non-local and non-Hamiltonian. Isomathematics was constructed in such a way to reconstruct linearity on isospaces over isofields. In fact, when you go to the abstract level, the non-linear isoproduct H(r, p)T(ψ*,...)ψ* can be written in the isolinear form , H(r, p) × ψ*, namely, a form which is linear on isospaces over isofields, but its projection tin on conventional spaces over conventional fields is non-linear. This is due to the fact that all non-linear terms are embedded in the isounit I(ψ*,...) =1/T(ψ*,...) > 0 that, being positive-definite, is topologically equivalent to the conventional unit "1", thus explaining why non-linearity disappear at the abstract level. I hope these comments have been of assistance in your study of a basic aspect in the search of new advances. Ruggero Maria Santilli (Email; research@thunder-energies.com).

Post 7
Prof. Santilli, hoping not to abuse your courtesy and time, please provide some information on the structure of the isoelectronium, such as the characteristics of the valence electrons when members of the isoelectroniumc. Vdr39yu<.p>

Post 8
Hello Vdr39yu - Post 7, thanks for an additional quite important question. Unfortunately, my knowledge of the structure of the isoelectronium is rather limited because I was satisfied by the fact that the isoelectronium as a quasi-particle allowed an exact representation if molecular data that could only be approximately represented with quantum chemistry. However, most of the research done for the constituents in the synthesis of the neutron from the proton and the electron applies to the constituents of the isoelectronium. Here are a few comments.

According to the 20th century physics of point-particles in vacuum, 'particles' are unitary irreducible representation of the Lorentz-Poincare' symmetry,. The neutron synthesis has established that, in the transition from motion in vacuum to motion within hyperdense hadronic matter, particle experience a mutation of their 'intrinsic' characteristics including mutations of their rest energy, spin, charge, magnetic moments, etc., in amount depending on local characteristics of the medium. As an example, for hadronic media of low density (such as that in the interior of mesons), conventional spin is expected to be conserved, while I consider purely political the idea that an electron maintains the spin 1/2 when immersed within media of very high density, such as that in the core of a star or in the interior of a black hole. The hierarchy of spin mutations is quantitatively treated in my 1998 proof of the EPR argument

In view of the indicated mutations, the constituents of the isoelectronium are not conventional electrons, but new particles called isoelectrons defined as isounitary isoirreducible isorepresentations of the Lorentz-Poincare'-Santilli isosymmetry on the the iso-Hilbert space over isofields, see the 1995 monograph Elements of Hadronic Mechanics, Volume II. As far as I can see, the spin and magnetic moment of the isoelectrons in the isoelectronium have conventional values, but I expect a mutation of their charge because potentially necessary to turn a Coulomb repulsion into an attraction. Hence the identical isoelectrons constituting the isoelectronium can be identified rather accurately via the isoirrep of the Lorentz-Poincare'-Santilli isosymmetry under the subsidiary constraints of recovering chemical molecular data. Sincerely, Ruggero Maria Santilli (Email: research@thunder-energies.com).

Post 9
Can anybody tell what is the rest energy of the isoelectronium? Ker34ui

Post 10
I studied Santilli's monograph on hadronic chemistry as well as his paper with Shillady, and my understanding is that the rest energy of the isoelectronium is not precisely known. This is due to the fact that: the sum of the rest energy of the two electron in vacuum is 1.022 MeV; binding energy (7) is very close to zero (for B = 1, n = 1, | E| = 0) because it is the binding energy caused by a "contact" interaction "not" derivable by a potential; and the contribution to the rest energy of the isoelectronium caused by the potential Coulomb interaction - at the risk of saying a "betise" - should give an "excess rest energy" over the value 1.022 MeV, since the interaction is repulsive (the contribution would be a routine mass defect in the event of an attraction). In any case, when compared to the stuffiness of orthodox chemistry, this is a quiet cool and refreshing problem indeed! Thank you, Santilli for peeking deep into nature. Swe57wo

Post 11
I Nominated Prof. Santilli for the Nobel Prize in Physics for his proof of the EPR argument, Post 13 of the preceding interview http://www.galileoprincipia.org/santilli-confirmation-of-the-epr-argument.php. After reading this interview and studying the related technical literature, I have Nominated Prof. Santilli also for the Nobel Prize in Chemistry hoping that he will be the second Nobel Laureate in both Physics and Chemistry after Madame Curie. Xer22uu

Post 12
Dear Prof. Santilli. You write: After years of trials and failures with conventional methods, I had to conclude that there is no possibility to achieve an attractive force between identical electrons via the use of the Schroedinger equation of quantum chemistry. Your approach consists in modifying the wave equation in such a way that you get the required results. It is the same approach followed by QCD. The problem with that kind of procedure is that the relation between theory and physical reality becomes more and more disconnected. I came to the conclusion that the crux of our model has its origin in the representation of particles in general. Representing particles as isolated entities in space makes it very difficult to explain interaction between them. My approach represents subatomic particles (SPs) as focal points of rays of Fundamental Particles (FPs) that extent from infinite to infinite. The energy of subatomic particles is distributed on their FPs as rotations defining longitudinal and transversal angular momenta. The interaction between SPs is the product of the interactions of the angular momenta of their FPs. One important conclusion is that electrons and positrons neither attract nor repel each other with the distance between them tending to zero. The nucleons can so be seen as a swarm of electrons and positrons and so the atomic nuclei. If the non-Hamiltonian interaction can be associated with the nucleus as a swarm of electrons and positrons,a physical explanation would support your mathematical approach. Dwe89pe

Post 13
Dear Dwe89pe / Post 12, I tried to reach Prof. Santilli for comments but he is out of contact for travel. Allow me to ex press my view and experience. I am so glad to see that you have been initially attracted by the 20th century scientific trap, pass to QFT whenever you have problems, but then you have identify its limitations. They are so many to justify the words "scientific trap." You pass from equations admitting analytic solution. to non-linear equations that can be manipulated at will. Then you have these divergencies so strenuously opposed by Paul Dirac for which "numerical results" are fake. Etc. I received copy of a momentous exchange back in 2007. Following the publication at Nuovo Cimento of Prof. santilli 50 years of work on the Lie-admissible generalization of QM to represent time irreversible systems, http://www.santilli-foundation.org/docs//Lie-admiss-NCB-I.pdf an academic guru contacted Prof. Santilli claiming that the Lie-admissible generalization is not necessary since QFT can represent time irreversibility (sic!!), how?, via the usual fake science, you throw here a Green distribution with arbitrary parameter and forma factors manipulated 'ad hoc', etc. You should see the river of disqualification provide by Prof. Santilli against this academician. Tye biggest problem of the 20th century physics you touch - but do not identify fully - is the representation of particles as point in vacuum, hence solely admitting potential interactions. the problem for the 20th century science is that, as stated by Prof. Santilli: The actual size of the wavepacket of one electron is as big as the entire universe, this implying that the universe is one single interconnected body characterized by an extremely large number of entanglements of wavefunctions whose sole communication is that of contact, non-linear, non-local and non-Hamiltonian interactions that can be solely treated via a generalizations of 20th century applied mathematics such as isomathematics. .. The entanglement of electron pairs becomes detectable by our limited instruments only at 1 Fermi distances, at which identical valence electrons can indeed bond to each other when in singlet coupling, resulting in the birth of molecules. I think you see everything in this statement, i.e., the need to: represent particles/wavepackets as extended; the need to admit in their overlapping the most general known non-Hamiltonian interactions; and the need for their serious treatment via a generalization of 20th century mathematics beginning most importantly with generalization of Newton's differential calculus from points to volumes http://www.santilli-foundation.org/docs/Santilli-37.pdf What you should do to write a truye page of new physics is to construct the hadronic field theory (HFT) because its foundations are the corerct one for extended particles, you will have no divergencies and see the quantum plane below from a much toller mointain, etc.ood luck Swe37ro

Post 14
I always thought that the measurement of the prediction by Bell proved that the quantum reality CANNOT be described by a theory with hidden variables and thus the theory of quantum mechanics is really as ``weird as the reality''. Can the author comment on whether his theory is in agreement with Bell inequalities? Nsd57ao

Post 15
Dear Nsd57ao // Post 14, thank you for your question. For the answer, please inspect the quoted preceding interview. You will see there that Prof. Santilli confirmed the full validity of Bell's inequality for point-particles in vacuum under sole potential interactions, while confirmed Einstein's vision that classical determinism is recovered for extended particles within physical media under non-linear, non-local and non-potential interactions. To technically understand the proof available in the 1998 paper
R. M. Santilli, "Isorepresentation of the Lie-isotopic SU(2) Algebra with Application to Nuclear Physics and Local Realism," Acta Applicandae Mathematicae Vol. 50, 177 (1998), http://www.santilli-foundation.org/docs/Santilli-27.pdf
you need to study the Lie-Santilli isotheory from the quoted literature. Above all, Prof. Santilli follows Einstein's main view namely, that quantum mechanics is indeed fully valid under the conditions implemented in its basic axioms (point particles in vacuum), but the belief that quantum mechanics describes all possible conditions existing in the universe is non-scientific, hence the need for its 'completion.' Best wishes. Fwe12io

Post 16
I am fascinated by Prof. Santilli's new isomathematics because of its capability of clearly representing in a concretely the actual size, shape and density of particles under the most general known interactions, see the preceding interview, particularly Post 8 and ffg in the comments. In Eq (6) of that post have seen the only representation I know of nuclei as a collection of "extended" nucleons. No wonder Prof. Santilli has achieved the first known exact representation of the synthesis of the neutron from the hydrogen as occurring in the core of stars, nuclear magnetic moments, nuclear spins and other nuclear data quantum mechanics has been unable to represent in one century.. Good job, Prof. Santilli. Bdf26yu

Post 17
Prof. Santilli, after reading your paper http://www.santilli-foundation.org/docs/Santilli-27.pdf I would like one of my graduate students do his Ph. D. Thesis on the completion of quantum mechanics into hadronic mechanics and its applications. Could you please recommend a list of primary mathematical, theoretical and experimental references and perhaps be part of the committee? Thanks Mrt89p

Post 18
Dear Colleague Mrt89p, I feel honored by your interest in our studies. Here are mu suggestions for a Ph. D. Thesis on the "completion" ofd quantum mechanics along Einstein's 1935 arguments:

1) Mathematical foundations: The first mandatory step is a study of the isotopic "completion" of 20th century. An introductory reading is the 1995 special issue of the Rendiconti containing my article on the general presentation and a second article on the "completion" of the Lie theory [1]. After that study, a recommend monograph [2] for a more technical knowledge of the new isomathematics. Independent mathematical works are available in refs. [3,4,5].

2) Theoretical Foundations. Following and only following a knowledge of the novel isomathematics, it is important to reach a knowledge of the isotopic completion of quantum mechanics into hadronic mechanics for which I recommend monograph [6]. Independent studies are available from monographs [7,8] containing vast specialized references on individual aspects.

3) Experimental verifications. Following the achievement of the necessary mathematical and theoretical knowledge, it is crucial to complete the study with experimental verifications available in various fields of physics, chemistry and biology, for which I recommend the recent review [9], particularly Sections 2 and 3, and original experimental works quoted therein.

Needless to say, I would be honored to be parti of the Poh. D. Thesis Committee as an external advisor for whatever I can do to help. Sincerely, Ruggero Santilli, Email: research@thunder-energies.com

References
[1] P. Vetro, Editor, Special Issue of rendiconti Circolo Matematico Palermo, Supplement. Vol. 42, 7-82 (1996),
http://www.santilli-foundation.org/docs/Santilli-37.pdf

[2] R. M. Santilli, Elements of Hadronic Mechanics, Vol. I Mathematical Foundations, Academy of Sciences, Kiev (1995)
http://www.santilli-foundation.org/docs/Santilli-300.pdf

[3] Chun-Xuan Jiang, Foundations of Santilli Isonumber Theory, International Academic Press (2001),
http://www.i-b-r.org/docs/jiang.pdf

[4] D. S. Sourlas and G. T. Tsagas, Mathematical Foundation of the Lie-Santilli Theory, Ukraine Academy of Sciences (1993),
http://www.santilli-foundation.org/docs/santilli-70.pdf

[5] S. Georgiev, Foundations of the IsoDifferential Calculus, Volumes, I, II, III, IV,V, and VI Nova Scientific Publisher (2015 on).

[6] R. M. Santilli, Elements of Hadronic Mechanics,, Vol. II Theoretical Foundations,, Academy of Sciences, Kiev, (1995)
http://www.santilli-foundation.org/docs/Santilli-301.pdf

[7] J. V. Kadeisvili, Santilli's Isotopies of Contemporary Algebras, Geometries and Relativities, Ukraine Academy of Sciences, Second edition (1997),
http://www.santilli-foundation.org/docs/Santilli-60.pdff

[8] I. Gandzha and J. Kadeisvili,
New Sciences for a New Era: Mathematical, Physical and Chemical Discoveries of Ruggero Maria Santilli,} Sankata Printing Press,\\ Nepal (2011),
http://www.santilli-foundation.org/docs/RMS.pdf

[9] R. M. Santilli "An introduction to the new sciences for a new era," Invited paper, SIPS 2016, Hainan Island, China Clifford Analysis, Clifford Algebras and their Applications Vol. 6, No. 1, pp. 1-119, 2017
http://www.santilli-foundation.org/docs/new-sciences-new-era.pdf

Post 19
One of my graduate students would like to do his Ph. D. Thesis on Santilli's IsoMathematics. Can anybody provide some basic references? Thanks. Bsd38ty

Post 20
EDITORIAL NOTE: We were unable to reach Prof. Santilli because on travel. As far as we know, the best references on the indicated Ph. D. Thesis is the
Ph. D. Course in IsoMathematics

Post 21
I believe that Santilli does not understand the current dominant view of covalence bonds that has worked so well for about one century. I do not see the value of this scientific fuzz of new mathematics and new chemistry. What's their benefits? Ker28fg

Post 22
Hi Dwe89pe / Post 12, you address the real historical issue Thanks. Einstein, Podolski and Rosen conclude their historical paper EPR Argument with the statement: While we have thus shown that the wave function does not provide a complete description of the physical reality, we left open the question of whether or not such a description exists. We believe, however, that such a theory is possible Prof. Santilli has done exact that, shown that, under a proper new dynamics for interior systems, the wave function is modified in such a way to approach classical determinism as it is the case for the two electrons of the pseudoproton, the two electron in covalence bonds, and other cases. Lfg38ty.

Post 23
Prof. Santilli, please express your view on the "EPR Paradox" as outlined, for instance, in the website https://www.thoughtco.com/epr-paradox-in-physics-2699186 Thank you. Ysr39ui


Figure 7. A conceptual view of the entanglement of particles characterized by contact non-Hamiltonian interactions due the overlapping of their wavepackets with ensuing continuous communication without superluminal speeds.

Post 24
Dear Ysr39ui / Post 23, thank you for raising such a pertinent question. In my view, the main issue of the debate on the 'EPR paradox' is that none of the participants, including Einstein, Bohr, Bohm, Bell, and others, identified the basic assumptions of quantum mechanics underlying their claims which are essentially the following:

1) The strictly point-like characterization of particles, which is inherent in the basic calculus underlying the treatment of the paradox, Newton's differential calculus, which can be solely formulated at isolated points. The paradox of superliuminal speed in particle 'entanglements' is then a mere consequence. In my view, the EPR paradox disappears when particles and their wavepackets are admitted to be extended and actually filling up the entire universe, of course, in a way rapidly decreasing with the distance. Hence, particles are continuously and permanently 'entangled' with their wavepackets, as illustrated in Figure 7, thus having continuous communications without any need of superluminal speeds and related violation of special relativity.

2) The sole admission of interactions derivable from a potential, that is, of Lagrangian/Hamiltonian type. It appears that the 'entanglement' of wavepackets causes a 'contact interaction,' that is one without potential energy which has, nevertheless, physical implications as it is the case for a balloon moving in our atmosphere. Following decades of search, I illustrated the interactions between entangled wavepackets in the chemical notion of valence. According to quantum mechanics and chemistry, identical electrons in singlet valence coupling must repel, rather than attract each other due to their equal charge and magnetic moments. After studies I initiated in the late 1970s when I was at Harvard University, I finally achieved in the late 1990s the 'attractive' force between identical valence electrons in one way and one way only, via the entanglement of their wavepackets, called 'deep mutual penetration' in the related literature (see this debate and the the 2001 monograph Foundations of Hadronic Chemistry). Besides the achievement of the first known exact representation if experimental data for the hydrogen and water molecules, the identification of an attractive force between valence electrons has permitted a deeper understanding of molecules, with the ensuing new HyperCombustion for the complete combustion of fossil fuels, which is under development by the U. S. publicly traded company Thunder Energies Corporation

3) Insufficiency of 20th century mathematics for a consistent treatment of entangled particles. As indicated earlier, entanglements effects are strictly non-potential. Additionally, entanglement effects are strictly non-local because defined over large volumes. The treatment of entanglements via the mathematics of quantum mechanics is grossly insufficient because said mathematics is solely definable at isolated points while the entanglement volumes cannot be reduced to a finite number of isolated points. Finally, entanglement effects are non-linear, that is, depending on power and derivatives of the wavefunctions. The biggest problem of the EPR paradox is the lack of admission that 20th century mathematics simply cannot treat non-linear, non-local and non-potential effects. For this reason, I initiated at Harvard University in the late 1970s the construction of a 'completion' of 20thy century applied mathematics into a form, today known as isomathematics. which has been conceived and constructed for the representation invariant over time of non-linear, non-local and non-potential effects. The main idea is truly elementary and consists in the generalization of all conventional product AB of arbitrary quantities A, B into the axiom-preserving, thus isotopic form ATB where T is a positive definite quantity providing the invariant representation of the extended character of wavepackets and their non-Hamiltonian interactions (see the 1978 monographs Foundations of Theoretical Mechanics, Volume I and Volume II). This initial formulation turned out to be 'incomplete' because not leaving invariant the unit '1' of the numeric field , thus requiring its formulation on numbers n* = n1* with arbitrary unit 1* = 1/T known as isonumbers All the above efforts continued to remain 'incomplete' because, by far, the most dominant limitation of quantum mechanics is its formulation via Newton's differential calculus, with consequential approximation of particles as isolated points. Following decades of trial and errors, I finally achieved in 1996 the 'completion' of Newton's differential calculus into a form today known as the isodifferential calculus. in which Newton's differential 'dr' is generalized into the broader form d*r* = Td(r 1*) = dr + rTd1*, with related derivatives, allowing the transition from the differential 'dr' at the isolated point 'r' to the isodifferential 'd*r* = Td(r1*)' which is defined over the volume T. The identification of a truly attractive force between entangled valence electrons was solely possible thanks to the use of isomathematics, and the same goes for numerous applications and experimental verifications (see the recent general review.

4) The general belief of the lack of existence of hidden variables. An important branch of isomathematics is the 'completion' of Lie's algebras with historical brackets [A, B] = AB - BA at the bass of the Copenhagen interpretation of quantum mechanics, into the iso-Lie algebras (see the recent review and original contributions quoted therein) with generalized brackets [A, B]* = ATB - BTA. Bohr 'hidden variables' can then be introduced very easily with the realization T = Diag. (λ, 1/λ). In the 1998 paper proof of the EPR argument, I presented the consequential inapplicability (and not the violation) of Bell's inequality for entangled wavepackets and the confirmation of the EPR Argument. The point to be stressed here is that the above concrete and explicit realization of hidden variables is achieved under the full validity of quantum axioms, solely subjected to a broader realization since the abstract axioms of mathematics and isomathematics, as well as Lie theory and iso-Lie theory, are the same. What we have in reality is an interpretation of quantum mechanics broaden than the Copenhagen form, today known as hadronic mechanics (see the 1995 monographs Elements of Hadronic Mechanics, Volume I: Mathematical Foundations. and Volume II: Theoretical Foundations).

5) Insufficient interest for experimental verifications and industrial applications of the EPR argument. All studies here considered originated from the inability of quantum mechanics to achieve any quantitative representation of Rutherford's synthesis of the neutron from a proton and an electron inside a star for numerous technical reasons. The representation of the neutron synthesis was solely possible via the EPR completion of quantum into hadronic mechanics and the resolution of the EPR paradox. Industrial equipment synthesizing neutrons on demand from a hydrogen gas are now in production and sale by Thunder Energies Corporation (see the TEC Directional Neutron Source). It seems reasonable that no in depth study of entanglements can be done without due consideration of the experimental and industrial applications of the 'completion' of 20th century sciences into covering views. Thunder Energies Corporation has funds to support nuclear physics laboratories interested in additional experimental tests and industrial applications of the ultimate process at the origin of stars, the synthesis of the neutron from the hydrogen. Ruggero Maria Santilli, email: research(at)thunder-energies(dot)com

Post 25
Prof. Santilli, thanks for the only true novelty I have seen in physics since I started my graduate studies. Congrats. I understand that : a) contact interactions, i.e., mutual penetration, entanglements, of wavepackets constitute true interactions causing physical effects; b) being pure Hamiltonian, QM cannot possibly represent such contact/penetration/entanglements, thus necessarily requiring Einstein's completion of QM; and c) I believe that your completion of QM by upgrading products AB into the axiom-preserving form ATB, T > 0, for all aspects of QM is brilliant, as illustrated by your proof that QM axioms do admit Bohm hidden variables λ. I am puzzled by a point you repeat in your writing, namely, that to have physical value representations have to be invariant over time. Could you please elaborate that point? Great thanks. Csd28ty

Post 26
Hi Csd28ty/Post 25, what a deep and sound question! Thanks for asking it. Yes, in my view any completion of QM has physical value if and only if the represented effects are invariant over time, that is, under the same physical conditions he numerical predictions must be invariant under the time evolution of the theory. The time evolution of Hadronic Mechanics (HM) is non-unitary when projected in the conventional Hilbert space over conventional fields. in fact, the iiso-Heisenberg equation

idA/dt = [A, H]* = ATH - HTA       (9)

is the infinitesimal form of the non-unitary transformations

A(t) = U(t)A(0)U(t) = eHTtiA(0)e-itTH ,       (10)

U(t)U(t) ≠ I.       (11)

The deep point you address that mandates the rejection of the above completion of QM is that time evolution (10) changes the numeric value of the isotopic element T = Diag. (λ, 1/λ) representing the entanglement of particles, as you can easily verify,

U(ATH - HTA)U = A' T' H' - H' T' A',   &emsp T' ≠ T.       (12)

However time evolution (9)-(11) is not that of HM. The correct Einstein completion of QM mandates its formulation on isospaces over isofields, in which case tine evolution (10) is iso-unitary,namely, it reconstructs unitarity on isospaces over isofields

U'*U' = u'*U' = E = 1/T > 0      (13)

where A*B = ATB and E is the fundamental isounit of the theory, thus implying U' - U, etc. You can then prove with simple calculations that the isotopic element is invariant under isounitary transforms,

U'*(A'*H')*U' = A"*H" - H"*A" = A"TH" = H"TA".       (14)

thus implying that the correct formulation of the completion of QM into HM, that via the use of isomathematics, does indeed [reserve over time of the numerical value of the isounit E = 1/T, thus implying the invariance over time of the entanglement of particles. This is the reason that, in my decades of studies to prove the EPR argument. I spent 80% of my time in the development of isomathematics. The physics came out as a consequence in a simple and unique form. In the event you want to study HM I recommend you should spend most of your time in the study of isomathematics, e.g., from my book 1995 monograph Elements of Hadronic Mechanics, Volume I: Mathematical Foundations. The understanding of -Volume II: Theoretical Foundations would be elementary. Then you will be several notches above your physics colleagues. Regards. R. M. Santilli

Post 27
Csd28ty/Post 25 and other colleagues dealing in time invariant formulations may be interested to know that such an invariance was achieved at the top Lie-admissible leve for irreversible processes as well as at the Lie-isotopic level for closed-isolated systems, in the paper below. Cheers. Ldf24pw
R. M. Santilli, "Invariant Lie-admissible formulation of quantum deformations," Found. Phys. {\bf 27}, 1159- 1177 (1997)
-http://www.santilli-foundation.org/docs/Santilli-06.pdf

Post 28
Interesting read, especially post 23 and 24.. Prof. Santilli States: In my view, the EPR paradox disappears when particles and their wavepackets are admitted to be extended and actually filling up the entire universe, of course, in a way rapidly decreasing with the distance. Hence, particles are continuously and permanently 'entangled' with their wavepackets, as illustrated in Figure 7, thus having continuous communications without any need of superluminal speeds and related violation of special relativity. I came to the same conclusion back in 2010 by interpreting Ezekiel's wheel within a wheel metaphor. Note that when we look at Fig. 7 above, we see "wheels within wheels." According to my interpretation of Ezekiel's occult texts, the wheel represents the particle's electric field and moves exactly with the particle. In other words, it is a nonlocal phenomenon that essentially fills the universe, as you write. Einstein and mainstream physicists are 100% wrong in their claim that the electric field propagates at c. The photons emitted by an electron (parent) are entangled with it and maintain a pure spherical relation with it at all times. These photons can be thought of as having the shape of the surface of a sphere. The likelihood of them interacting with other particles diminishes with the square of their distance from their source/parent particle. The same text in the book of Ezekiel also indicates that the electron consists of four sub-particles acting as one. Each sub-particle has 1/4 electric charge. Here's my blog article on this topic if anyone is interestedhttps://rebelscience.blogspot.com/2010/09/lattice-interactions-part-ix_16.html Der56io

Post 29
The topics covered by this web site reflects the viewpoint on quantum mechanics as derived from classical mechanics. Classical mechanics works at a scale circa 1 m. Quantum mechanics operates at the atom scale, 10^{-8} m. When we approaching the scale 10^{-8} m something happens in space, such that we find ourselves in a miracle. But we also know the minimum physical size, namely, Planck's length 10^{-35} m and researchers are inclined to think that at this scale physical space has a cellular structure. Therefore, if we try to develop quantum mechanics starting from this scale, will quantum mechanics look also so unusual? The problem was studied in my book entitled Structure of Space and the Submicroscopic Deterministic Concept of Physics, here is the announcement on the web site of the publishers: http://www.appleacademicpress.com/structure-of-space-and-the-submicroscopic-deterministic-concept-of-physics-/9781771885300 The studies easily solve the situation associated with the EPR Argument because instead of one quantum system we reveal a system of two connected sub quantum systems, namely, the particle and a cloud of spatial excitations that accompany the particle... (and by the way, Prof. Santilli's works helped me to obtain several correct results).

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